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Simplifying 45a2 + 42ab + -24b2 = 0 Reorder the terms: 42ab + 45a2 + -24b2 = 0 Solving 42ab + 45a2 + -24b2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3'. 3(14ab + 15a2 + -8b2) = 0 Factor a trinomial. 3((5a + -2b)(3a + 4b)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5a + -2b)' equal to zero and attempt to solve: Simplifying 5a + -2b = 0 Solving 5a + -2b = 0 Move all terms containing a to the left, all other terms to the right. Add '2b' to each side of the equation. 5a + -2b + 2b = 0 + 2b Combine like terms: -2b + 2b = 0 5a + 0 = 0 + 2b 5a = 0 + 2b Remove the zero: 5a = 2b Divide each side by '5'. a = 0.4b Simplifying a = 0.4bSubproblem 2
Set the factor '(3a + 4b)' equal to zero and attempt to solve: Simplifying 3a + 4b = 0 Solving 3a + 4b = 0 Move all terms containing a to the left, all other terms to the right. Add '-4b' to each side of the equation. 3a + 4b + -4b = 0 + -4b Combine like terms: 4b + -4b = 0 3a + 0 = 0 + -4b 3a = 0 + -4b Remove the zero: 3a = -4b Divide each side by '3'. a = -1.333333333b Simplifying a = -1.333333333bSolution
a = {0.4b, -1.333333333b}
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